IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i16p3517-d1217244.html
   My bibliography  Save this article

Adaptive Consensus of the Stochastic Leader-Following Multi-Agent System with Time Delay

Author

Listed:
  • Shoubo Jin

    (School of Mathematics and Statistics, Suzhou University, Suzhou 234000, China)

  • Guanghui Zhang

    (School of Mathematics and Statistics, Suzhou University, Suzhou 234000, China)

Abstract

For the multi-agent system with time delay and noise, the adaptive consensus of tracking control problems is discussed by the Lyapunov function. The main purpose of this study is to design an adaptive control protocol for the system, such that even if there exists time delay among agents, the protocol can still ensure the consensus of the stochastic system. The main contribution is to revise the protocols that were previously only applicable to system without time delay. Because the system is inevitably disrupted by time delay and noise during the interactive process, achieving coordination and consensus is difficult. To enable the followers to track the leader, a novel adaptive law depending on the Riccati equation is firstly proposed, and the adaptive law is different from previous mandatory control law completely depending on a known function. The ability to be altered online based on the state of system is a major feature of the adaptive law. When there are interactive noise and time delay between the followers and leader of the system, a special Lyapunov function is constructed to prove the adaptive consensus. And the upper bound of time delay is obtained by using the Itô integral theory. Finally, if the time delay of the system approaches zero, it is shown that the adaptive law still ensures that each follower tracks the leader under simpler conditions.

Suggested Citation

  • Shoubo Jin & Guanghui Zhang, 2023. "Adaptive Consensus of the Stochastic Leader-Following Multi-Agent System with Time Delay," Mathematics, MDPI, vol. 11(16), pages 1-18, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3517-:d:1217244
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/16/3517/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/16/3517/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jeong, Juyoung & Lim, Yongdo & Parivallal, Arumugam, 2023. "An asymmetric Lyapunov-Krasovskii functional approach for event-triggered consensus of multi-agent systems with deception attacks," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    2. Hu, Jiangping & Hong, Yiguang, 2007. "Leader-following coordination of multi-agent systems with coupling time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 853-863.
    3. Shoubo Jin & Qiuju Yu & Siew Ann Cheong, 2021. "Construction of Adaptive Consensus Gains for Multiagent Systems with Multiplicative Noise," Complexity, Hindawi, vol. 2021, pages 1-11, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Long Jian & Yongfeng Lv & Rong Li & Liwei Kou & Gengwu Zhang, 2023. "Distributed Disturbance Observer-Based Containment Control of Multi-Agent Systems via an Event-Triggered Approach," Mathematics, MDPI, vol. 11(10), pages 1-12, May.
    2. Jian, Long & Hu, Jiangping & Wang, Jun & Shi, Kaibo, 2019. "Observer-based output feedback distributed event-triggered control for linear multi-agent systems under general directed graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    3. Jing Bai & Guoguang Wen & Ahmed Rahmani & Xing Chu & Yongguang Yu, 2016. "Consensus with a reference state for fractional-order multi-agent systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(1), pages 222-234, January.
    4. Ruan, Xiaoli & Xu, Chen & Feng, Jianwen & Wang, Jingyi & Zhao, Yi, 2022. "Adaptive dynamic event-triggered control for multi-agent systems with matched uncertainties under directed topologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).
    5. Baojie Zheng & Xiaowu Mu, 2016. "Formation-containment control of second-order multi-agent systems with only sampled position data," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(15), pages 3609-3618, November.
    6. Yang, Yang & Wang, Xue & Wu, Yingcheng & Yue, Wenbin, 2023. "Dynamic average consensus control based on event-triggered cloud access," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    7. Peng, Zhinan & Hu, Jiangping & Shi, Kaibo & Luo, Rui & Huang, Rui & Ghosh, Bijoy Kumar & Huang, Jiuke, 2020. "A novel optimal bipartite consensus control scheme for unknown multi-agent systems via model-free reinforcement learning," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    8. Xi, Jianxiang & Shi, Zongying & Zhong, Yisheng, 2012. "Admissible consensus and consensualization of high-order linear time-invariant singular swarm systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5839-5849.
    9. Guo, Wanli & He, Wennuo & Shi, Lili & Sun, Wen & Lu, Xiaoqing, 2021. "Fixed-time consensus tracking for nonlinear stochastically disturbed multi-agent systems via discontinuous protocols," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    10. Zhao, Can & Liu, Xinzhi & Zhong, Shouming & Shi, Kaibo & Liao, Daixi & Zhong, Qishui, 2021. "Leader-following consensus of multi-agent systems via novel sampled-data event-triggered control," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    11. Mo, Lipo & Yuan, Xiaolin & Yu, Yongguang, 2018. "Target-encirclement control of fractional-order multi-agent systems with a leader," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 479-491.
    12. Xiaole Xu & Lixin Gao, 2016. "Intermittent observer-based consensus control for multi-agent systems with switching topologies," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(8), pages 1891-1904, June.
    13. Xianyong Zhang & Yaohong Huang & Li Li & Wei-Chang Yeh, 2018. "Power and Capacity Consensus Tracking of Distributed Battery Storage Systems in Modular Microgrids," Energies, MDPI, vol. 11(6), pages 1-25, June.
    14. Wu, Zhihai & Peng, Li & Xie, Linbo & Wen, Jiwei, 2013. "Stochastic bounded consensus tracking of leader–follower multi-agent systems with measurement noises based on sampled-data with small sampling delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 918-928.
    15. He, Xiaoyan & Wang, Qingyun & Yu, Wenwu, 2015. "Finite-time distributed cooperative attitude tracking control for multiple rigid spacecraft," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 724-734.
    16. Zhang, Jiangbo & Hong, Yiguang, 2013. "Opinion evolution analysis for short-range and long-range Deffuant–Weisbuch models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5289-5297.
    17. Xi, Lei & Yu, Tao & Yang, Bo & Zhang, Xiaoshun & Qiu, Xuanyu, 2016. "A wolf pack hunting strategy based virtual tribes control for automatic generation control of smart grid," Applied Energy, Elsevier, vol. 178(C), pages 198-211.
    18. Wu, Jie & Deng, Qun & Han, Tao & Yang, Qing-Sheng & Zhan, Heng, 2019. "Bipartite tracking consensus for multi-agent systems with Lipschitz-Type nonlinear dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1360-1369.
    19. Mo, Lipo & Niu, Yuguang & Pan, Tingting, 2015. "Consensus of heterogeneous multi-agent systems with switching jointly-connected interconnection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 132-140.
    20. Jian, Long & Hu, Jiangping & Wang, Jun & Shi, Kaibo, 2019. "Distributed event-triggered protocols with Kx-functional observer for leader-following multi-agent systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3517-:d:1217244. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.